Question

Please help me find each function?

Answer 1

See answers below

Explanation:

Given: `f(x) = 1/(2x); " "g(x) = x^2; " "h(x) = x-8; " "k(x) = sqrt(x)`

There are two ways to find the answers, first find the combined function and then evaluate the combined function or evaluate each function individually and then combine:

1) `(gk)(x) = x^2sqrt(x); " "(gk)(4) = 4^2 sqrt(4) = 16*2 = 32`

`" or " g(4) = 4^2=16; " "k(4) = sqrt(4) = 2`

`" "(gk)(4) = g(4)*k(4)=32`

2) `(g + h)(x) = g(x) + h(x) = x^2 + x - 8`

`" "(g+h)(5) = 5^2 + 5-8 = 22`

`" or " (g + h)(5) = g(5) + h(5) = 5^2 + 5-8 = 22`

3)`(g/k)(x) = x^2/sqrt(x); " "(g/k)(9) = 9^2/sqrt(9) = 81/3 = 27`

`" or "(g/k)(9) = (g(9))/(k(9)) = 81/3 = 27`

4)`f(h(x)) = 1/(2(x-8)); " "f(h(1)) = 1/(2*(1 - 8)) = -1/14`

`" or "h(1) = -7; " "f(-7) = 1/(2*-7) = -1/14`