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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...

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 = meannumber of students = 905 = 450 and the ∑marks for th...

Answered by Ryan S. • Maths tutor

3153 Views

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

dy/dx = tan³(x)sec²(x)

Integrate both sides ==> ∫dy= ∫ tan³(x)sec²(x) dx

Use the substitution u=tan(x)

And by different...

Answered by Ryan S. • Maths tutor

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

In order to solve this equation (x²-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. There...

Answered by Arrthe N. • Maths tutor

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