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# Given f^-1(x)= 1100(1.02)^x, Solve f(x)=0?

Solve please show work

### 1 Answer

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- ChameleojackLv 57 years agoBest Answer
This is the inverse-function, so first we need to find the function.

f⁻¹(x) = 1100(1.02)ˣ

y = 1100(1.02)ˣ

switch x and y

x = 1100(1.02)^y

x/1100 = 1.02^y

log(x/1100) = log(1.02^y)

log(x/1100) = y·log(1.02)

y = log(x/1100)/log(1.02)

f(x) = log(x/1100)/log(1.02)

now let f(x) = 0 and solve for x:

0 = log(x/1100)/log(1.02)

0·log(1.02) = log(x/1100)

0 = log(x/1100)

10⁰ = 10^(log(x/1100))

1 = x/1100

x = 1100

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