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Math Help - URGENT help required=Uni Maths Homework

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    Exclamation URGENT help required=Uni Maths Homework

    Hi there, i am in need of some urgent help for my maths homework. It has to be handed in within ten hours and i really need help with the following:
    (*= to the power of)

    1. Find the inverse of the function given by f(x)=4x-7

    2.a. Given that y=3logb 4-2logb 8-logb 3 express y as a single logarithm to base b. Find the value of y when b=3

    2.b. Suppose that (2x+a)3*=px3* + qx2* + 150x -125. Using the third row of Pascal's triangle(or otherwise) find the value of a, p and q

    3. Consider these two functions: f(x)= 3/x-4 x cannot be equaled to 4 and g(x)=x2 (squared)


    a) find the inverse function f-1(x) and clearly state any values of x for which the inverse is not defined
    b) find the composite functions f o g (x) and g o f (x) , clearly stating any values of x for which these composites are not defined.




    please help, any feedback appreciated.

    Colin
    x
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  2. #2
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    Quote Originally Posted by twowoundedbirds View Post
    Hi there, i am in need of some urgent help for my maths homework. It has to be handed in within ten hours and i really need help with the following:
    (*= to the power of)

    1. Find the inverse of the function given by f(x)=4x-7
    From f:y=4x-7 you'll get f^{-1}: x = 4y-7

    Solve this equation for y.

    2.a. Given that y=3logb 4-2logb 8-logb 3 express y as a single logarithm to base b. Find the value of y when b=3
    Use the log rules:

    y = 3\log_b(4)-2\log_b(8)-\log_b(3)=\log_b(2^6)-\log_b(2^6)-\log_b(3)=-\log_b(3)

    If b = 3 then y = -1

    ...

    3. Consider these two functions: f(x)= 3/x-4 x cannot be equaled to 4 and g(x)=x2 (squared)


    a) find the inverse function f-1(x) and clearly state any values of x for which the inverse is not defined
    b) find the composite functions f o g (x) and g o f (x) , clearly stating any values of x for which these composites are not defined.

    ...
    to a) Determine domain and range of f. Then you know the domain and range of f^{-1} too. Swap x for y to get the equation of f^{-1}.

    Only for the records: f^{-1}(x)=\dfrac{3+4x}x

    to b)

    (f\circ g)(x)=f(g(x))=\dfrac3{x^2-4},~x\ne-2~\vee~x\ne2

    (g\circ f)(x)=(g(f(x))=\left(\dfrac3{x-4}\right)^2,~x\ne4
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