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

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sorry i couldnt figure out how to the squared and such lol :/

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.4Assuming your question is given:\[g(x)=2x^28\]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:\[g(x)=2x^28\]\[g(x)+8=2x^2\]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 righthandside with x, and replace the x on the lefthandside 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:\[g(x)=2x^28\]\[g(2)=2*(2)^28=2*48=88=0\]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.
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