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Thread: Two function questions....

  1. #1
    M23
    M23 is offline
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    Two function questions....

    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!
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  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
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    Good Night.

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

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

    So you are correct

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