Which two functions are inverses of each other? A. f(x) = x, g(x) = –x B. f(x) = 2x, g(x) = -1/2x C. f(x) = 4x, g(x) = 1/4x D. f(x) = –8x, g(x) = 8x

Answer:The correct option is C) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]Step-by-step explanation: We need to find out the pair of functions which are inverse of each otherA) [tex]f(x)=x \ \text{and} \ g(x)=-x[/tex]   Since, [tex](fog)(x)=f(g(x))=-x[/tex]    and   [tex](gof)(x)=g(f(x))=-x[/tex]     So, these are not inverse of each othersB) [tex]f(x)=2x \ \text{and} \ g(x)=\frac{-x}{2}[/tex]   Since, [tex](fog)(x)=f(g(x))=2(\frac{-x}{2})=-x[/tex]    and   [tex](gof)(x)=g(f(x))=\frac{-2x}{2}=-x[/tex]     So, these are not inverse of each othersC) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]   Since, [tex](fog)(x)=f(g(x))=4(\frac{x}{4})=x[/tex]    and   [tex](gof)(x)=g(f(x))=\frac{4x}{4}=x[/tex]     So, these are inverse of each othersD) [tex]f(x)=-8x \ \text{and} \ g(x)=8x[/tex]   Since, [tex](fog)(x)=f(g(x))=-8(8x)=-64x[/tex]    and   [tex](gof)(x)=g(f(x))=8(-8x)=-64x[/tex]     So, these are not inverse of each othersTherefore the correct option is C) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]