Question

given the functions f(x) and g(x) below, find indicated composition.
f(x)=18x+7
g(x)=x^3
find g^-1 o f^-1 (493)
help how can i solve? show steps please

Answer 1

inverse of y=f(x) is gotten from switching x and y
y = 18 x + 7 becomes
x = 18 y + 7 and solve this
so
y = (x-7)/18 = f^-1 (x), the inverse

I don't know the f o g operation.

Answer 2

I'm going to type this problem statement out in Equation Editor for greater clarity.\[g ^{-1}(x) ~o ~f ^{-1}(493)\] This is called a "composite function;" the second function becomes the input to the first.

Answer 3

i see so the inverse of 18x+7 get pluged into the x for x^3?

Answer 4

I'd prefer that we work through the intermediary steps before I answer that question.

If f(x) = 18x+7, how would you go about finding the inverse function, \[f ^{-1}(x)?\]

Similarly: if g(x) = x^3, how would you find\[g ^{-1}(x)?~ g ^{-1}(493)?\]

Answer 5

so to inverse f(x)=18x+7
x=18y+7
y=x-7/18?

Answer 6

i'm having trouble on the second part of the questions. Can you help explain what I need to do?

Answer 7

Find the inverse of each f(x) and g(x). Your result for f(x) would be correct if you typed it like this:\[f ^{-1}(x)=\frac{ x-7 }{ 18 }~or ~\frac{ (x-7) }{ 18 }.\]

Answer 8

Hold this. Now, focus on g(x). You must ALSO find the inverse function of g(x). Would you do that now, please?\[g ^{-1}(x)=?\]

Answer 9

Next, replace the x in \[f ^{-1}(x) =\frac{ x-7 }{ 18 }\]
with \[g ^{-1}(x)=?\]

And, finally, replace x in the resulting expression with 493.

As much as I'd like to continue helping you, Jon, it's my bedtime! If no one else has helped you by morning, I'll be on OpenStudy again tomorrow morning.

Answer 10

okay goodnight thank you for ur help :)

Answer 11

Good night to you also, John Le!