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Math  /  Algebra

QuestionLet f(x)=x2−3x,g(x)=x+7f(x)=x^{2}-\frac{3}{x}, g(x)=\sqrt{x+7}. Find f(g(2))f(g(2))

Studdy Solution

STEP 1

1. We are given two functions: f(x)=x2−3x f(x) = x^2 - \frac{3}{x} and g(x)=x+7 g(x) = \sqrt{x+7} .
2. We need to find the value of f(g(2)) f(g(2)) .

STEP 2

1. Evaluate g(2) g(2) .
2. Substitute the result from Step 1 into f(x) f(x) .
3. Calculate f(g(2)) f(g(2)) .

STEP 3

Evaluate g(2) g(2) :
g(2)=2+7 g(2) = \sqrt{2 + 7}

STEP 4

Simplify the expression inside the square root:
g(2)=9 g(2) = \sqrt{9}

STEP 5

Calculate the square root:
g(2)=3 g(2) = 3

STEP 6

Substitute g(2)=3 g(2) = 3 into f(x) f(x) :
f(g(2))=f(3)=32−33 f(g(2)) = f(3) = 3^2 - \frac{3}{3}

STEP 7

Simplify the expression:
f(3)=9−1 f(3) = 9 - 1

STEP 8

Calculate the result:
f(3)=8 f(3) = 8
The value of f(g(2)) f(g(2)) is:
8 \boxed{8}

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