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Math  /  Algebra

QuestionGiven that f(x)=2x+3f(x)=2 x+3 and h(x)=x3h(x)=x^{3}, find (h∘f)(2)(h \circ f)(2). (h∘f)(2)=(h \circ f)(2)= □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. We are given two functions: f(x)=2x+3 f(x) = 2x + 3 and h(x)=x3 h(x) = x^3 .
2. We need to find the value of the composite function (h∘f)(2)(h \circ f)(2).

STEP 2

1. Understand the composition of functions.
2. Compute f(2) f(2) .
3. Substitute the result of f(2) f(2) into h(x) h(x) .
4. Compute h(f(2)) h(f(2)) .

STEP 3

Understand that (h∘f)(x)(h \circ f)(x) means h(f(x)) h(f(x)) . This means we first apply f(x) f(x) and then apply h(x) h(x) to the result of f(x) f(x) .

STEP 4

Compute f(2) f(2) by substituting x=2 x = 2 into f(x) f(x) :
f(2)=2(2)+3 f(2) = 2(2) + 3

STEP 5

Simplify the expression for f(2) f(2) :
f(2)=4+3 f(2) = 4 + 3 f(2)=7 f(2) = 7

STEP 6

Substitute f(2)=7 f(2) = 7 into h(x) h(x) to find h(f(2)) h(f(2)) :
h(f(2))=h(7)=73 h(f(2)) = h(7) = 7^3

STEP 7

Compute h(7) h(7) :
h(7)=73=343 h(7) = 7^3 = 343
The value of (h∘f)(2)(h \circ f)(2) is:
343 \boxed{343}

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