SOLUTION: Verify that the function g(z)=(x-2)/5 is the inverse function of f(x)=5x+2. Show your work.

Algebra ->  Functions -> SOLUTION: Verify that the function g(z)=(x-2)/5 is the inverse function of f(x)=5x+2. Show your work.      Log On


   

Question 175584: Verify that the function g(z)=(x-2)/5 is the inverse function of f(x)=5x+2. Show your work.
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Verify that the function g(x)=(x-2)/5 is the inverse function of f(x)=5x+2
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Show that f[g(x)] = x and that g[f(x)]=x
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f[g(x)] = f[(x-2)/5] = 5[(x-2)/5}+2 = x-2+2 = x
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g[f(x)] = g[5x+2] = (5x+2-2)/5 = 5x/5 = x
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Cheers,
Stan H.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse, switch to x,y notation.
+f%28x%29=5%2Ax%2B2+
+y=5%2Ax%2B2
Now interchange x and y and solve for y.
+y=5%2Ax%2B2
+highlight%28x%29=5%2Ahighlight%28y%29%2B2
5y=x-2
y=%28x-2%29%2F5
This new y is the inverse function, g.
g%28x%29=%28x-2%29%2F5
It matches the given inverse function.