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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
3847 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
12906 Views

Describe the similarities and differences between simple diffusion, facilitated diffusion and active transport.

Simple diffusion, facilitated diffusion and active transport are three methods to transport various molecules across a membrane. Whilst similar in the overall effect, there are some major differences between...
JG
Answered by James G. • Biology tutor
83482 Views

I'm very nervous about the speaking exam - I'm afraid that I won't know what to talk about as it's not an easy paper to revise. How do I go about handling mental blocks during the exam?

This is a question many nervous A Level French students ask throughout the academic year after they’ve found out that there is a big jump between GCSE and A Level French. Three elements can be identified in ...
RC
Answered by Rosen C. • French tutor
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