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Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)

(a) Start with f(x)= 3x − 5; y=3x - 5, and switch x and y before rearanging to get y in terms of x again: y=3x - 5 x=3y - 5 (x+5)/3=y Therefore f^−1(x)=(x+5)/3 (b) Start with f(x)= 3x − 5 and and sub result ...
IB
Answered by Isobel B. • Maths tutor
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5 students are in a maths class and 10 students are in a physics class. The mean mark of the maths class is 90 and the mean mark of the physics class is 85. Work out the mean mark of both classes.

To find the mean mark the formula is mean = ∑marks /number of students Therefore the mean for maths is 90 and so ∑marks = mean number of students = 90 5 = 450 and the ∑marks for the physics class is 85*10= 8...
RS
Answered by Ryan S. • Maths tutor
3852 Views

Solve the differential equation: dy/dx = tan^3(x)sec^2(x)

dy/dx = tan 3 (x)sec 2 (x) Integrate both sides ==> ∫dy= ∫ tan 3 (x)sec 2 (x) dx Use the substitution u=tan(x) And by differentiation du/dx = sec 2 (x) , which leads to dx = du/sec 2 (x) ==> and subbin...
RS
Answered by Ryan S. • Maths tutor
12914 Views

Solve this quadratic equation by factorising: x^2-x-6=0

In order to solve this equation (x 2 -x-6=0) using the factorising method, you should first find the two numbers that mutiply to -6 and add to -1. The two numbers that do this are 2 and -3. Therefore, (x+2) ...
AN
Answered by Arrthe N. • Maths tutor
4938 Views

Hairdresser A charges £66 for a haircut and has an offer of 1/3rd off. Hairdresser B charges £70 for a haircut and has an offer of 20% off. Which hairdresser is cheaper?

Hairdresser A as they charge £44 wheras Hairdresser B charges £56
EN
Answered by Ellen N. • Maths tutor
3288 Views