Question

If f(x) = x^2, g(x) = 5x, and h(x) = x + 4, find each value. Show work and explain please for both problems
14. [fo(hog)](-1)
15. [fo(goh)](4)

Answer 1

@Mertsj

Answer 2

[fo(hog)](-1) is the same as saying f [ h(g(-1)) ]

Answer 3

so

step 1) find g(-1)

step 2) plug the result from step 1 into h(x)

step 3) plug the result of step 2 into f(x)

this will give you your final answer for #14

Answer 4

# 15 is the exact same as #14 but now you're using the functions in a different order and you're using a different initial input

Answer 5

Can you do #14 with me and let me do #15 on my own? @jim_thompson5910

Answer 6

sure

Answer 7

ok first step is to find g(-1)

Answer 8

we just replace each x with -1 in g(x), then evaluate

g(x) = 5x

g(-1) = 5(-1)

g(-1) = -5

Answer 9

that will turn

f [ h(g(-1)) ]

into

f [ h(-5) ]

Answer 10

now find h(-5)

Answer 11

h(x) = x + 4

h(-5) = -5 + 4

h(-5) = -1

Answer 12

so

f [ h(-5) ]

becomes

f [ -1 ]

Answer 13

sorry my allergies are making it hard to see things <--- watery eyes + nose

Answer 14

last step is to find f(-1)

f(x) = x^2

f(-1) = (-1)^2

f(-1) = 1

Answer 15

so in the end,

f [ h(g(-1)) ] = 1

ie

[fo(hog)](-1) = 1

Answer 16

@jim_thompson5910 Thanks so much! :D I actually know how to do it