Two function questions....

**M23** · June 27th 2009, 02:50 PM

Given f(x)= sq2x+7 and g(x)=x^2-1 , then the value of g[f(1)] is

A. 8
B.(sq7)
C. 0
D. 2

I think this one is B, but am not sure....

And the second one...

7. If the equation of a function is y=f(x)=1/2x-5 then the equation of y=f^-1(x) is

A. y = 2x + 10
B. y = 2x + 5

C. y=-1/2x +5

D. y=1/2x-10

Thanks for any help!

**I-Think** · June 27th 2009, 03:04 PM

Good Night.

Number 1.
$f(x)= \sqrt{2x+7}, g(x)=x^2-1$

Find the value of $f(1)$
$f(1)=\sqrt{2(1)+7}$
$=3$
Find $g(3)$
$g(3)=3^2-1$
$=8$

So you are correct

Number 2.
$y=f(x)=\frac{1}{2}x-5$
To find $y=f^{-1}(x)$ , exchange the $y$ and $x$ in $f(x)$
So we now have $x=\frac{1}{2}y-5$
Make $y$ the subject of the formula
$x+5=\frac{1}{2}y$
$2x+10=y$
$f^{-1}(x) =2x+10$
Ans:A

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