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QuestionFind g(f(5x))g(f(5 x)) for f(x)=2x−1f(x)=2 x-1 and g(x)=3x2−7g(x)=3 x^{2}-7. Choices: A. 150x2−15150 x^{2}-15 B. 300x2−60x−4300 x^{2}-60 x-4 C. 60x3−60x2−20x60 x^{3}-60 x^{2}-20 x D. 750x3−75x2−70x+7750 x^{3}-75 x^{2}-70 x+7 E. 30x4−15x3−70x2+35x30 x^{4}-15 x^{3}-70 x^{2}+35 x

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x) is defined as f(x)=x−1f(x)=x-1 . The function g(x)g(x) is defined as g(x)=3x−7g(x)=3x^{}-7
3. We need to find the value of g(f(5x))g(f(5x))

STEP 2

First, we need to find the value of f(5x)f(5x). We can do this by substituting 5x5x into the function f(x)f(x).
f(5x)=2(5x)−1f(5x) =2(5x) -1

STEP 3

Now, simplify the expression to find the value of f(5x)f(5x).
f(5x)=10x−1f(5x) =10x -1

STEP 4

We now have the value of f(x)f(x). Next, we need to find the value of g(f(x))g(f(x)). We can do this by substituting f(x)f(x) into the function g(x)g(x).
g(f(x))=g(10x−1)g(f(x)) = g(10x -1)

STEP 5

Substitute 10x−110x -1 into the function g(x)g(x).
g(10x−1)=3(10x−1)2−7g(10x -1) =3(10x -1)^{2} -7

STEP 6

Now, simplify the expression to find the value of g(10x−1)g(10x -1).
g(10x−1)=3(100x2−20x+1)−g(10x -1) =3(100x^{2} -20x +1) -

STEP 7

Expand the brackets and simplify the expression.
g(10x−1)=300x2−60x+3−7g(10x -1) =300x^{2} -60x +3 -7

STEP 8

implify the expression to get the final value of g(f(5x))g(f(5x)).
g(f(5x))=300x2−60x−4g(f(5x)) =300x^{2} -60x -4So, the correct answer is 300x2−60x−4300x^{2} -60x -4.

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