Given $f^{-1}(x)=400(1.02)^{x}$, what is $f(x)$ ?
A) $\frac{\sqrt[x]{1.02}}{400}$
B) $ 1.02 \sqrt[x]{400}$
C) $\frac{\ln (x)-\ln (1.02)}{\ln (400)}$
D) $\frac{\ln (x)-\ln (400)}{\ln (1.02)}$

Question

Quizplus · Accepted Answer

The inverse function $f^{-1}(x)$ is given, so to find $f(x)$, we need to solve for $x$ in terms of $y$ from the equation $y = 400(1.02)^{x}$. Solving for $x$, we get $x = \frac{\ln(y) - \ln(400)}{\ln(1.02)}$, which corresponds to option D.

Given f−1(x)=400(1.02)xf^{-1}(x)=400(1.02)^{x}f−1(x)=400(1.02)x , What Is f(x)f(x)f(x) ? A) 1.02x400\frac{\sqrt[x]{1.02}}{400}400x1.02​​ B) 1.02400x 1.02 \sqrt[x]{400}1.02x400​ C) ln⁡(x)−ln⁡(1.02)ln⁡(400)\frac{\ln (x)-\ln (1.02)}{\ln (400)}ln(400)ln(x)−ln(1.02)​

Given $f^{-1}(x)=400(1.02)^{x}$ , What Is $f(x)$ ?
A) $\frac{\sqrt[x]{1.02}}{400}$ B) $1.02 \sqrt[x]{400}$ C) $\frac{\ln (x)-\ln (1.02)}{\ln (400)}$