Question

For which pairs of functions is (f*g)(x)=12x?

Answer 1

D!!!!!

Explanation:

Just took the test

Answer 2

Answer: f(x) = 4x and g(x) = 3x

Explanation:

`\text{ If }f(x) = 3 - 4x \text{ and } g(x) = 16x-3`

`\implies (fog)(x) = f[g(x)] = f(16x-3) = 3-4(16x-3)=3-64x+12=15-64x\\eq 12x`

`\text{ If } f(x) = 6x^2 \text{ and }g(x) =(2)/(x)`

`\implies (fog)(x) = f[g(x)] = f((2)/(x)) = 6((2)/(x))^2=(24)/(x^2)\\eq 12x`

`\text{ If } f(x) = √(x)\text{ and } g(x) = 144x`

`\implies (fog)(x) = f[g(x)] = f(144x) = √(144x)=12√(x)\\eq 12x`

`\text{ If }f(x) = 4x \text{ and } g(x) = 3x`

`\implies (fog)(x) = f[g(x)] = f(3x) = 4(3x)=12x=12x`

Hence, Fourth pair of function f(x) and g(x) is giving (fog)=12x.