Question

State if the given functions are inverses. 1) F(x)=1/2x -2 g(x) = 2x + 4

Answer 1

Answer:

Yes

Step-by-step explanation:

• if $f(x)=\frac{1}{2}x-2$ then what is $f^-1(x)$  (the inverse of f(x)? let's find out
• $f(x)=\frac{1}{2}x-2\\y=\frac{1}{2}x-2$ make f(x) into y
• Then make y into x and make x into y so $x=\frac{1}{2}y-2$
• $x=\frac{1}{2}y-2$ now get the new y on the left and everything else on the right
• $x=\frac{1}{2}y-2\\x+2=\frac{1}{2}y\\2(x+2)=(2)\frac{1}{2}y\\y=2x+4$ now make y = g(x)
• $g(x)=2x+4$
• So you found the inverse of f(x) and it is the same as g(x), so the functions are inverses of each other