Math / Algebra

Question(3) Question \#18
Reference Q. 11243 For each pair of functions, write a formula for $g(f(x))$ . a. $f(x)=2-x, g(x)=|x+2|$ b. $f(x)=2 x+1, g(x)=x^{4}$ c. $f(x)=3^{x}, g(x)=x-1$

Studdy Solution

STEP 1

1. We are given pairs of functions $f(x)$ and $g(x)$ .
2. We need to find the composition of the functions, denoted as $g(f(x))$ .
3. The composition $g(f(x))$ means substituting $f(x)$ into $g(x)$ .

STEP 2

1. Understand the composition of functions.
2. Calculate $g(f(x))$ for each pair of functions.

STEP 3

Understand the composition of functions:
The composition $g(f(x))$ means that we take the output of $f(x)$ and use it as the input for $g(x)$ . In other words, wherever there is an $x$ in $g(x)$ , we replace it with $f(x)$ .

STEP 4

Calculate $g(f(x))$ for part (a):
Given: $f(x) = 2 - x$ $g(x) = |x + 2|$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(2 - x) = |(2 - x) + 2| = |4 - x|$

STEP 5

Calculate $g(f(x))$ for part (b):
Given: $f(x) = 2x + 1$ $g(x) = x^4$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(2x + 1) = (2x + 1)^4$

STEP 6

Calculate $g(f(x))$ for part (c):
Given: $f(x) = 3^x$ $g(x) = x - 1$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(3^x) = 3^x - 1$
The formulas for $g(f(x))$ are: a. $|4 - x|$ b. $(2x + 1)^4$ c. $3^x - 1$

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Question(3) Question \#18
Reference Q. 11243 For each pair of functions, write a formula for $g(f(x))$ . a. $f(x)=2-x, g(x)=|x+2|$ b. $f(x)=2 x+1, g(x)=x^{4}$ c. $f(x)=3^{x}, g(x)=x-1$

Studdy Solution

STEP 1

1. We are given pairs of functions $f(x)$ and $g(x)$ .
2. We need to find the composition of the functions, denoted as $g(f(x))$ .
3. The composition $g(f(x))$ means substituting $f(x)$ into $g(x)$ .

STEP 2

1. Understand the composition of functions.
2. Calculate $g(f(x))$ for each pair of functions.

STEP 3

Understand the composition of functions:
The composition $g(f(x))$ means that we take the output of $f(x)$ and use it as the input for $g(x)$ . In other words, wherever there is an $x$ in $g(x)$ , we replace it with $f(x)$ .

STEP 4

Calculate $g(f(x))$ for part (a):
Given: $f(x) = 2 - x$ $g(x) = |x + 2|$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(2 - x) = |(2 - x) + 2| = |4 - x|$

STEP 5

Calculate $g(f(x))$ for part (b):
Given: $f(x) = 2x + 1$ $g(x) = x^4$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(2x + 1) = (2x + 1)^4$

STEP 6

Calculate $g(f(x))$ for part (c):
Given: $f(x) = 3^x$ $g(x) = x - 1$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(3^x) = 3^x - 1$
The formulas for $g(f(x))$ are: a. $|4 - x|$ b. $(2x + 1)^4$ c. $3^x - 1$

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Studdy Solution

STEP 1

1. We are given pairs of functions f(x) f(x) f(x) and g(x) g(x) g(x).2. We need to find the composition of the functions, denoted as g(f(x)) g(f(x)) g(f(x)).3. The composition g(f(x)) g(f(x)) g(f(x)) means substituting f(x) f(x) f(x) into g(x) g(x) g(x).

STEP 2

1. Understand the composition of functions.2. Calculate g(f(x)) g(f(x)) g(f(x)) for each pair of functions.

STEP 3

Understand the composition of functions:The composition g(f(x)) g(f(x)) g(f(x)) means that we take the output of f(x) f(x) f(x) and use it as the input for g(x) g(x) g(x). In other words, wherever there is an x x x in g(x) g(x) g(x), we replace it with f(x) f(x) f(x).

STEP 4

STEP 5

Calculate g(f(x)) g(f(x)) g(f(x)) for part (b):Given: f(x)=2x+1 f(x) = 2x + 1 f(x)=2x+1 g(x)=x4 g(x) = x^4 g(x)=x4Substitute f(x) f(x) f(x) into g(x) g(x) g(x): g(f(x))=g(2x+1)=(2x+1)4 g(f(x)) = g(2x + 1) = (2x + 1)^4 g(f(x))=g(2x+1)=(2x+1)4

STEP 6

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1. We are given pairs of functions $f(x)$ and $g(x)$ .
2. We need to find the composition of the functions, denoted as $g(f(x))$ .
3. The composition $g(f(x))$ means substituting $f(x)$ into $g(x)$ .

1. Understand the composition of functions.
2. Calculate $g(f(x))$ for each pair of functions.

Understand the composition of functions:
The composition $g(f(x))$ means that we take the output of $f(x)$ and use it as the input for $g(x)$ . In other words, wherever there is an $x$ in $g(x)$ , we replace it with $f(x)$ .

Calculate $g(f(x))$ for part (b):
Given: $f(x) = 2x + 1$ $g(x) = x^4$
Substitute $f(x)$ into $g(x)$ : $g(f(x)) = g(2x + 1) = (2x + 1)^4$