Graph f(x)=`log_(5)(x+5)` Label your graph Find g(x), the inverse of f(x)=`` Add g(x) to your graph and label, draw the line of symmetry on your graph as a dashed line Please help me with this...

Graph f(x)=`log_(5)(x+5)`

  • Label your graph

Find g(x), the inverse of f(x)=``

Add g(x) to your graph and label, draw the line of symmetry on your graph as a dashed line


Please help me with this problem!! I cant figure it out for the life of me

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

Fisrt find the inverse function. By the definition of the inverse function, we have to solve for x the equation f(x) = y:

log_5_(x+5) = y.

Apply 5^() to both sides (we can do this because 5^x is one-to-one function):

(x+5) = 5^y  (5^[log_5_(a)] = a by definition of log_5).

Now we easily obtain x = g(y) = 5^y - 5. If we want g=g(x) then
g(x) = 5^x - 5.

For graphing, use computer (although we know how these graphs look in general). None of these graphs have line of symmetry, but they are symmetrical to each other with respect to the line y=x. It is true for any function h and its inverse p: if (x, h(x)) is at the graph of h, then the symmetric point (h(x), x) = (h(x), p(h(x))) is at the graph of p.

I hope this will help you.

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