Math / Algebra

QuestionComposition of functions
COPY - Let $f(x)=2 x-1, g(x)=3 x$ , and $h(x)=x^{2}+1$ . Find $g(f(0))$

Studdy Solution

STEP 1

1. We are given three functions: $f(x) = 2x - 1$ , $g(x) = 3x$ , and $h(x) = x^2 + 1$ .
2. We need to find the value of the composition $g(f(0))$ .

STEP 2

1. Evaluate the function $f(x)$ at $x = 0$ .
2. Use the result from Step 1 as the input for the function $g(x)$ .
3. Calculate $g(f(0))$ .

STEP 3

Evaluate $f(x)$ at $x = 0$ :
$f(0) = 2(0) - 1$

STEP 4

Simplify the expression:
$f(0) = 0 - 1$ $f(0) = -1$

STEP 5

Use the result from Step 1 as the input for $g(x)$ :
$g(f(0)) = g(-1)$

STEP 6

Evaluate $g(x)$ at $x = -1$ :
$g(-1) = 3(-1)$

STEP 7

Simplify the expression:
$g(-1) = -3$
The value of $g(f(0))$ is:
$\boxed{-3}$

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QuestionComposition of functions
COPY - Let $f(x)=2 x-1, g(x)=3 x$ , and $h(x)=x^{2}+1$ . Find $g(f(0))$

Studdy Solution

STEP 1

1. We are given three functions: $f(x) = 2x - 1$ , $g(x) = 3x$ , and $h(x) = x^2 + 1$ .
2. We need to find the value of the composition $g(f(0))$ .

STEP 2

1. Evaluate the function $f(x)$ at $x = 0$ .
2. Use the result from Step 1 as the input for the function $g(x)$ .
3. Calculate $g(f(0))$ .

STEP 3

Evaluate $f(x)$ at $x = 0$ :
$f(0) = 2(0) - 1$

STEP 4

Simplify the expression:
$f(0) = 0 - 1$ $f(0) = -1$

STEP 5

Use the result from Step 1 as the input for $g(x)$ :
$g(f(0)) = g(-1)$

STEP 6

Evaluate $g(x)$ at $x = -1$ :
$g(-1) = 3(-1)$

STEP 7

Simplify the expression:
$g(-1) = -3$
The value of $g(f(0))$ is:
$\boxed{-3}$

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QuestionComposition of functionsCOPY - Let f(x)=2x−1,g(x)=3xf(x)=2 x-1, g(x)=3 xf(x)=2x−1,g(x)=3x, and h(x)=x2+1h(x)=x^{2}+1h(x)=x2+1. Find g(f(0))g(f(0))g(f(0))

Studdy Solution

STEP 1

1. We are given three functions: f(x)=2x−1 f(x) = 2x - 1 f(x)=2x−1, g(x)=3x g(x) = 3x g(x)=3x, and h(x)=x2+1 h(x) = x^2 + 1 h(x)=x2+1.2. We need to find the value of the composition g(f(0)) g(f(0)) g(f(0)).

STEP 2

1. Evaluate the function f(x) f(x) f(x) at x=0 x = 0 x=0.2. Use the result from Step 1 as the input for the function g(x) g(x) g(x).3. Calculate g(f(0)) g(f(0)) g(f(0)).

STEP 3

Evaluate f(x) f(x) f(x) at x=0 x = 0 x=0:f(0)=2(0)−1 f(0) = 2(0) - 1 f(0)=2(0)−1

STEP 4

Simplify the expression:f(0)=0−1 f(0) = 0 - 1 f(0)=0−1 f(0)=−1 f(0) = -1 f(0)=−1

STEP 5

Use the result from Step 1 as the input for g(x) g(x) g(x):g(f(0))=g(−1) g(f(0)) = g(-1) g(f(0))=g(−1)

STEP 6

Evaluate g(x) g(x) g(x) at x=−1 x = -1 x=−1:g(−1)=3(−1) g(-1) = 3(-1) g(−1)=3(−1)

STEP 7

Simplify the expression:g(−1)=−3 g(-1) = -3 g(−1)=−3 The value of g(f(0)) g(f(0)) g(f(0)) is:−3 \boxed{-3} −3​

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QuestionComposition of functions
COPY - Let $f(x)=2 x-1, g(x)=3 x$ , and $h(x)=x^{2}+1$ . Find $g(f(0))$

1. We are given three functions: $f(x) = 2x - 1$ , $g(x) = 3x$ , and $h(x) = x^2 + 1$ .
2. We need to find the value of the composition $g(f(0))$ .

1. Evaluate the function $f(x)$ at $x = 0$ .
2. Use the result from Step 1 as the input for the function $g(x)$ .
3. Calculate $g(f(0))$ .

Evaluate $f(x)$ at $x = 0$ :
$f(0) = 2(0) - 1$

Simplify the expression:
$f(0) = 0 - 1$ $f(0) = -1$

Use the result from Step 1 as the input for $g(x)$ :
$g(f(0)) = g(-1)$

Evaluate $g(x)$ at $x = -1$ :
$g(-1) = 3(-1)$

Simplify the expression:
$g(-1) = -3$
The value of $g(f(0))$ is:
$\boxed{-3}$