Solved on Sep 17, 2023

Find $h(x)=2x+3$ , then simplify (i) $h(a+3)$ and (ii) $h(2b)$ . Also, find the value of $a$ such that $h(a+3)=5$ .

STEP 1

Assumptions1. The function $h$ is defined by $h(x)=x+3$ . We are asked to find expressions for $h(a+3)$ and $h(b)$ 3. We are also asked to find the value of $a$ such that $h(a+3)=5$

STEP 2

We start by finding the expression for $h(a+)$ . We do this by replacing $x$ in the function definition with $a+$ .
$h(a+) =2(a+) +$

STEP 3

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(a+3) =2a +6 +3$

STEP 4

Combine like terms to simplify the expression further.
$h(a+3) =2a +9$

STEP 5

Next, we find the expression for $h(2b)$ . We do this by replacing $x$ in the function definition with $2b$ .
$h(2b) =2(2b) +3$

STEP 6

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(2b) =4b +3$

STEP 7

Now we find the value of $a$ such that $h(a+3)=5$ . We do this by setting $h(a+3)$ equal to $5$ and solving for $a$ .
$h(a+3) =5$ $2a +9 =5$

STEP 8

Subtract $$ from both sides of the equation to isolate $2a$.
$2a =5 -$

STEP 9

implify the right side of the equation.
$2a = -4$

STEP 10

Divide both sides of the equation by $2$ to solve for $a$ .
$a = -4 /2$

STEP 11

implify the right side of the equation to find the value of $a$ .
$a = -$ So, the value of $a$ such that $h(a+3)=5$ is $-$ .

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Find $h(x)=2x+3$ , then simplify (i) $h(a+3)$ and (ii) $h(2b)$ . Also, find the value of $a$ such that $h(a+3)=5$ .

STEP 1

Assumptions1. The function $h$ is defined by $h(x)=x+3$ . We are asked to find expressions for $h(a+3)$ and $h(b)$ 3. We are also asked to find the value of $a$ such that $h(a+3)=5$

STEP 2

We start by finding the expression for $h(a+)$ . We do this by replacing $x$ in the function definition with $a+$ .
$h(a+) =2(a+) +$

STEP 3

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(a+3) =2a +6 +3$

STEP 4

Combine like terms to simplify the expression further.
$h(a+3) =2a +9$

STEP 5

Next, we find the expression for $h(2b)$ . We do this by replacing $x$ in the function definition with $2b$ .
$h(2b) =2(2b) +3$

STEP 6

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(2b) =4b +3$

STEP 7

Now we find the value of $a$ such that $h(a+3)=5$ . We do this by setting $h(a+3)$ equal to $5$ and solving for $a$ .
$h(a+3) =5$ $2a +9 =5$

STEP 8

Subtract $$ from both sides of the equation to isolate $2a$.
$2a =5 -$

STEP 9

implify the right side of the equation.
$2a = -4$

STEP 10

Divide both sides of the equation by $2$ to solve for $a$ .
$a = -4 /2$

STEP 11

implify the right side of the equation to find the value of $a$ .
$a = -$ So, the value of $a$ such that $h(a+3)=5$ is $-$ .

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Find h(x)=2x+3h(x)=2x+3h(x)=2x+3, then simplify (i) h(a+3)h(a+3)h(a+3) and (ii) h(2b)h(2b)h(2b). Also, find the value of aaa such that h(a+3)=5h(a+3)=5h(a+3)=5.

STEP 1

Assumptions1. The function hhh is defined by h(x)=x+3h(x)=x+3h(x)=x+3 . We are asked to find expressions for h(a+3)h(a+3)h(a+3) and h(b)h(b)h(b)3. We are also asked to find the value of aaa such that h(a+3)=5h(a+3)=5h(a+3)=5

STEP 2

We start by finding the expression for h(a+)h(a+)h(a+). We do this by replacing xxx in the function definition with a+a+a+.h(a+)=2(a+)+h(a+) =2(a+) +h(a+)=2(a+)+

STEP 3

Now we simplify the expression by distributing the 222 inside the parentheses.h(a+3)=2a+6+3h(a+3) =2a +6 +3h(a+3)=2a+6+3

STEP 4

Combine like terms to simplify the expression further.h(a+3)=2a+9h(a+3) =2a +9h(a+3)=2a+9

STEP 5

Next, we find the expression for h(2b)h(2b)h(2b). We do this by replacing xxx in the function definition with 2b2b2b.h(2b)=2(2b)+3h(2b) =2(2b) +3h(2b)=2(2b)+3

STEP 6

Now we simplify the expression by distributing the 222 inside the parentheses.h(2b)=4b+3h(2b) =4b +3h(2b)=4b+3

STEP 7

Now we find the value of aaa such that h(a+3)=5h(a+3)=5h(a+3)=5. We do this by setting h(a+3)h(a+3)h(a+3) equal to 555 and solving for aaa.h(a+3)=5h(a+3) =5h(a+3)=52a+9=52a +9 =52a+9=5

STEP 8

Subtract $$ from both sides of the equation to isolate $2a$.2a=5−2a =5 -2a=5−

STEP 9

implify the right side of the equation.2a=−42a = -42a=−4

STEP 10

Divide both sides of the equation by 222 to solve for aaa.a=−4/2a = -4 /2a=−4/2

STEP 11

implify the right side of the equation to find the value of aaa.a=−a = -a=−So, the value of aaa such that h(a+3)=5h(a+3)=5h(a+3)=5 is −-−.

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Find $h(x)=2x+3$ , then simplify (i) $h(a+3)$ and (ii) $h(2b)$ . Also, find the value of $a$ such that $h(a+3)=5$ .

Assumptions1. The function $h$ is defined by $h(x)=x+3$ . We are asked to find expressions for $h(a+3)$ and $h(b)$ 3. We are also asked to find the value of $a$ such that $h(a+3)=5$

We start by finding the expression for $h(a+)$ . We do this by replacing $x$ in the function definition with $a+$ .
$h(a+) =2(a+) +$

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(a+3) =2a +6 +3$

Combine like terms to simplify the expression further.
$h(a+3) =2a +9$

Next, we find the expression for $h(2b)$ . We do this by replacing $x$ in the function definition with $2b$ .
$h(2b) =2(2b) +3$

Now we simplify the expression by distributing the $2$ inside the parentheses.
$h(2b) =4b +3$

Now we find the value of $a$ such that $h(a+3)=5$ . We do this by setting $h(a+3)$ equal to $5$ and solving for $a$ .
$h(a+3) =5$ $2a +9 =5$

Subtract $$ from both sides of the equation to isolate $2a$.
$2a =5 -$

implify the right side of the equation.
$2a = -4$

Divide both sides of the equation by $2$ to solve for $a$ .
$a = -4 /2$

implify the right side of the equation to find the value of $a$ .
$a = -$ So, the value of $a$ such that $h(a+3)=5$ is $-$ .