if (f(x)=5x - 25) and (g(x)=\frac{1}{5}x + 5), which expression could be used to verify (g(x)) is the…

if (f(x)=5x - 25) and (g(x)=\frac{1}{5}x + 5), which expression could be used to verify (g(x)) is the inverse of (f(x))?\n(\frac{1}{5}(\frac{1}{5}x + 5)+5)\n(\frac{1}{5}(5x - 25)+5)\n(\frac{1}{(\frac{1}{5}x + 5)})\n(5(\frac{1}{5}x + 5)+5)

if (f(x)=5x - 25) and (g(x)=\frac{1}{5}x + 5), which expression could be used to verify (g(x)) is the inverse of (f(x))?\n(\frac{1}{5}(\frac{1}{5}x + 5)+5)\n(\frac{1}{5}(5x - 25)+5)\n(\frac{1}{(\frac{1}{5}x + 5)})\n(5(\frac{1}{5}x + 5)+5)

Answer

Explanation:

Step1: 逆関数の性質を利用

2つの関数$f(x)$と$g(x)$が互いに逆関数であるための条件は$f(g(x)) = x$または$g(f(x)) = x$です。ここでは$f(g(x))$を求めます。$f(x)=5x - 25$で$g(x)=\frac{1}{5}x + 5$です。$f(g(x))$を求めるには、$g(x)$の式を$f(x)$の$x$に代入します。 $f(g(x))=5(\frac{1}{5}x + 5)-25$ではなく、$g(f(x))$を求めると、$f(x)$の式を$g(x)$の$x$に代入します。$g(f(x))=\frac{1}{5}(5x - 25)+5$。

Answer:

$\frac{1}{5}(5x - 25)+5$