## anonymous 4 years ago if g(x) = 2x squared - 8, find g to the -1 power(x)

1. anonymous

sorry i couldnt figure out how to the squared and such lol :/

2. asnaseer

Assuming your question is given:$g(x)=2x^2-8$find $$g^{-1}(x)$$. g(x) gives you a value for g for a given value of x. $$g^{-1}(x)$$ gives you the inverse of this - i.e. given a value for g, what value of x produced this? so you need to get an expression for x in terms of g(x). the steps are as follows:$g(x)=2x^2-8$$g(x)+8=2x^2$therefore:$2x^2=g(x)+8$$x^2=\frac{g(x)+8}{2}$$x=\pm\sqrt{\frac{g(x)+8}{2}}$this is the inverse function and we usually replace g(x) on the right-hand-side with x, and replace the x on the left-hand-side with $$g^{-1}(x)$$ to get:$g^{-1}(x)=\pm\sqrt{\frac{x+8}{2}}$you can check if this is correct or not by trying some values. so lets calculate g for x=2:$g(x)=2x^2-8$$g(2)=2*(2)^2-8=2*4-8=8-8=0$now lets use this value of g to calculate $$g^{-1}$$:$g^{-1}(x)=\pm\sqrt{\frac{x+8}{2}}$$g^{-1}(0)=\pm\sqrt{\frac{0+8}{2}}=\pm\sqrt{\frac{8}{2}}=\pm\sqrt{4}=\pm2$so we can see that g has the value zero for either x=2 or x=-2.