Question

Can anyone help me with the following, by providing the steps to get there and what it is that you are doing? any help would be greatly appreciated...

We define the following functions:
f(x)=2x+5 g(x)=x^2-3 h(x)=7-x/3



◦Compute (f – h)(4).




◦Evaluate the following two compositions:
A: (fog)(x)
B: (hog)(x)




◦Graph the g(x) function and transform it so that the graph is moved 6 units to the right and 7 units down.

How do I figure out what these values are for the g(x)?




◦Find the inverse functions:
C: f^-1(x)
D: h^-1(x)

Answer 1

f(x)=2x+5 g(x)=x^2-3 h(x)=7-x/3

(f-h)(4) = f(4)-h(4) = 9-17/3 = 10/3
(f◦g)(x) = f(g) = 2g+5 = 2(x^2-3)+5 = 2x^2-1
(h◦g) = 7-g/3 = 7-(x^2-3)/3 = 8-x^2/3

g(x-6)-7 = (x-6)^2-3-7 = (x-6)^2-10
graph at wolframalpha.com

f^-1(x) = (x-5)/2
h^-1(x) = 21-3x