URGENT help required=Uni Maths Homework

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Originally Posted by twowoundedbirds

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.

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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

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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)

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

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