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cowboys93 · Jul 13, 2009, 07:23 PM

it says to show how f and g are inverse functions (a)algebraically(b)graphically
f(x)=x-5, g(x) x=5
Please helpppp I don't understand this.

allso it says to find the inverse function of f informally. Verify that f(f-1(x))=x and
f-1(f(x))=x
1.f(x)=1/3x

I tried this one and I don't know how to do it. I hate working with fractions.

please & thank you verryy muuchhh.:o

Unknown008 · Jul 14, 2009, 07:20 AM

You should know the relationship between a function and its inverse.

To make the inverse of a function, for example f(x) = 10x - 2, you let it be y = 10x - 2 and make x the subject of the formula.

$f(x) = 10x-2$

$y = 10x - 2$

$x = \frac{y+2}{10}$

Finally, replace x by $f^{-1}(x)$ which will represent the inverse of f(x) and replace y by x in your function;

$f^{-1}(x) = \frac{x+2}{10}$

That's it for algebraically.

For graphing, plot the two graphs. Inverse functions have some sort of 'mirror' line (or line of symmetry) along the line y=x. If they do have this property, then they are said to be the inverse of one another.

For the first part;

$f(f^{-1}(x)) = x$

replace $f^{-1}(x)$ by the f inverse you just had, that is;

$f(f^{-1}(x)) = f(x+5) = ((x+5) - 5)$

Can you try for the remaining ones now?