Math / Algebra

QuestionQuestion For the functions $f(x)=2 x+5$ and $g(x)=5 x^{2}$ , find $(f \circ g)(x)$ .
Provide your answer below:

Studdy Solution

STEP 1

1. We are given two functions, $f(x) = 2x + 5$ and $g(x) = 5x^2$ .
2. We need to find the composition of these functions, specifically $(f \circ g)(x)$ .

STEP 2

1. Understand the concept of function composition.
2. Substitute $g(x)$ into $f(x)$ .
3. Simplify the resulting expression.

STEP 3

Understand that $(f \circ g)(x)$ means $f(g(x))$ . This requires substituting the output of $g(x)$ into the input of $f(x)$ .

STEP 4

Substitute $g(x) = 5x^2$ into $f(x) = 2x + 5$ . This means replacing every $x$ in $f(x)$ with $g(x)$ .
$f(g(x)) = f(5x^2) = 2(5x^2) + 5$

STEP 5

Simplify the expression $2(5x^2) + 5$ .
$2 \times 5x^2 = 10x^2$
So, $f(g(x)) = 10x^2 + 5$ .

STEP 6

The simplified expression for $(f \circ g)(x)$ is:
$(f \circ g)(x) = 10x^2 + 5$
This is the final result of the function composition.

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QuestionQuestion For the functions $f(x)=2 x+5$ and $g(x)=5 x^{2}$ , find $(f \circ g)(x)$ .
Provide your answer below:

Studdy Solution

STEP 1

1. We are given two functions, $f(x) = 2x + 5$ and $g(x) = 5x^2$ .
2. We need to find the composition of these functions, specifically $(f \circ g)(x)$ .

STEP 2

1. Understand the concept of function composition.
2. Substitute $g(x)$ into $f(x)$ .
3. Simplify the resulting expression.

STEP 3

Understand that $(f \circ g)(x)$ means $f(g(x))$ . This requires substituting the output of $g(x)$ into the input of $f(x)$ .

STEP 4

Substitute $g(x) = 5x^2$ into $f(x) = 2x + 5$ . This means replacing every $x$ in $f(x)$ with $g(x)$ .
$f(g(x)) = f(5x^2) = 2(5x^2) + 5$

STEP 5

Simplify the expression $2(5x^2) + 5$ .
$2 \times 5x^2 = 10x^2$
So, $f(g(x)) = 10x^2 + 5$ .

STEP 6

The simplified expression for $(f \circ g)(x)$ is:
$(f \circ g)(x) = 10x^2 + 5$
This is the final result of the function composition.

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QuestionQuestion For the functions f(x)=2x+5f(x)=2 x+5f(x)=2x+5 and g(x)=5x2g(x)=5 x^{2}g(x)=5x2, find (f∘g)(x)(f \circ g)(x)(f∘g)(x).Provide your answer below:

Studdy Solution

STEP 1

1. We are given two functions, f(x)=2x+5 f(x) = 2x + 5 f(x)=2x+5 and g(x)=5x2 g(x) = 5x^2 g(x)=5x2.2. We need to find the composition of these functions, specifically (f∘g)(x) (f \circ g)(x) (f∘g)(x).

STEP 2

1. Understand the concept of function composition.2. Substitute g(x) g(x) g(x) into f(x) f(x) f(x).3. Simplify the resulting expression.

STEP 3

Understand that (f∘g)(x) (f \circ g)(x) (f∘g)(x) means f(g(x)) f(g(x)) f(g(x)). This requires substituting the output of g(x) g(x) g(x) into the input of f(x) f(x) f(x).

STEP 4

Substitute g(x)=5x2 g(x) = 5x^2 g(x)=5x2 into f(x)=2x+5 f(x) = 2x + 5 f(x)=2x+5. This means replacing every x x x in f(x) f(x) f(x) with g(x) g(x) g(x).f(g(x))=f(5x2)=2(5x2)+5 f(g(x)) = f(5x^2) = 2(5x^2) + 5 f(g(x))=f(5x2)=2(5x2)+5

STEP 5

Simplify the expression 2(5x2)+5 2(5x^2) + 5 2(5x2)+5.2×5x2=10x2 2 \times 5x^2 = 10x^2 2×5x2=10x2So, f(g(x))=10x2+5 f(g(x)) = 10x^2 + 5 f(g(x))=10x2+5.

STEP 6

The simplified expression for (f∘g)(x) (f \circ g)(x) (f∘g)(x) is:(f∘g)(x)=10x2+5 (f \circ g)(x) = 10x^2 + 5 (f∘g)(x)=10x2+5This is the final result of the function composition.

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QuestionQuestion For the functions $f(x)=2 x+5$ and $g(x)=5 x^{2}$ , find $(f \circ g)(x)$ .
Provide your answer below:

1. We are given two functions, $f(x) = 2x + 5$ and $g(x) = 5x^2$ .
2. We need to find the composition of these functions, specifically $(f \circ g)(x)$ .

1. Understand the concept of function composition.
2. Substitute $g(x)$ into $f(x)$ .
3. Simplify the resulting expression.

Understand that $(f \circ g)(x)$ means $f(g(x))$ . This requires substituting the output of $g(x)$ into the input of $f(x)$ .

Substitute $g(x) = 5x^2$ into $f(x) = 2x + 5$ . This means replacing every $x$ in $f(x)$ with $g(x)$ .
$f(g(x)) = f(5x^2) = 2(5x^2) + 5$

Simplify the expression $2(5x^2) + 5$ .
$2 \times 5x^2 = 10x^2$
So, $f(g(x)) = 10x^2 + 5$ .

The simplified expression for $(f \circ g)(x)$ is:
$(f \circ g)(x) = 10x^2 + 5$
This is the final result of the function composition.