Question

HELP! Write in inverse function notation (f^-1(x)).
1. f(x)= 5^x + 4

Answer 1

the inverse...means switch the x's and y's...then solve for y again

so take your

y=5^x + 4
and switch the x's and y's

so

x = 5^y + 4

now solve again for y

subtract 4 from both sides

x - 4 = 5^y

and use logs to get that exponent down so

log(x-4) = ylog5
now isolate y by dividing both sides by log5

y = log(x-4)/log5

i believe...anyone correct me if i'm wrong :)

Answer 2

Remember, the inverse of a function is a reflection over the line y = x. To find the inverse algebraically, simply switch y with the place of x and then solve for y. Like this:\[f(x)=y=5^x + 4 \rightarrow f^{-1}(x)=x=5^y+4\]Now solve for y.\[x=5^y+4\rightarrow x-4 = 5^y \rightarrow \log(x-4)=\log(5)^y \rightarrow \log(x-4)=y*\log(5)\]\[\rightarrow \frac{ \log(x-4) }{ \log(5) }=y \rightarrow y=\log _{5}(x-4)\]Therefore:\[f^{-1}(x):y=\log _{5}(x-4)\]

Answer 3

@Shiner