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Maths
A Level

f(x) = 2 / (x^2 + 2). Find g, the inverse of f.

Rewrite as y = 2 / (x^2 + 2). Swap all x and y symbols to create x = 2 / (y^2 + 2). Rearrange for y to reach y=g(x)=sqrt( (2-2x) / x ).

AR
Answered by Alfie R. Maths tutor
3312 Views

Given that y = 5x^3 + 7x + 3, find dy/dx

This is an example of differentiation. With differentiation the key rule that allows us to differentiate most algebraic functions is "times the coefficient by the power then decrease the power by one...

TT
Answered by Tej T. Maths tutor
4936 Views

If f(x) = (3x-2) / x-5 x>6, find a.) ff(8) b.) the range of f(x) c.) f^-1(x) and state its range.

Firstly, ff(8) is the same as f(f(8)) so f(8) needs to be found first. Subbing in x=8 f(8)=22/3, so f(22/3) is required, Setting x=22/3 f(22/3)= 20/(22/3 - 5) = 60/7. so ff(8)=60/7.Next, as x tends to in...

EF
Answered by Euan F. Maths tutor
4243 Views

f(x) = (sin(x))^3. What is f'(x)

Write sin3(x) as sin2x*sinx and differentiate using product rule, u=sin2x, v

LR
Answered by Liam R. Maths tutor
2774 Views

What is the integral of 2x^5 - 1/4x^3 - 5

Integrating is essentially the opposite of differentiating.xn --> xn+1 We add 1 to the power and re-introduce variables where they have been eliminated potentially k --> kxWe m...

JS
Answered by Joshua S. Maths tutor
3143 Views

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