Composition of Functions

Question

Let f(x)=3x^2, g(x)=9x-2, m(x)=4x, and r(x)=sqrt3x. Find and simplify the composite function.

1) r(g(x))----> I got sqrt(27x-6)

2) r(f(x))-----> I got 3x

3) g(m(f(x)))---> I got 108x^2

Are those right ?

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Identify the function f(x)

4) h(x) = e^f(x)=e^sinx----> I got sinx ??

5) k(x) = sin(f(x))= sin(x^3 +3x+1)

6) m(x)=ln f(x) =ln(5+1/x)

Answer 1

Composition of Functions

Let f(x)=3x^2, g(x)=9x-2, m(x)=4x, and r(x)=sqrt(3x).

Find and simplify the composite function.

1) r(g(x))----> I got sqrt(27x-6)
sqrt(3(9x-2)) You’re right.

2) r(f(x))-----> I got 3x
sqrt(3(3x^2)) You’re right.

3) g(m(f(x)))---> I got 108x^2
9(4(3x^2))-2 You need to tack on a –2.

Are those right ?
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Identify the function f(x)

4) h(x) = e^f(x) = e^sin(x) ——> I got sin(x) ??
Right.

5) k(x) = sin(f(x)) = sin(x^3 + 3x + 1)
It’s x^3 + 3x + 1.

6) m(x) = ln(f(x)) =ln(5+1/x)
It’s 5+1/x.