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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 ).

Answered by Alfie R. Maths tutor
3148 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...

Answered by Tej T. Maths tutor
4604 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...

Answered by Euan F. Maths tutor
3989 Views

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

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

Answered by Liam R. Maths tutor
2570 Views

A linear sequence is as follows: a+b, a+3b, a+5b .... The 2nd term is equal to 15. The 6th term is 47. What is the value of a? What is the value of b? Show your working.

a+3b = 15, a+11b=47 , use simultaneous equations to get 8b = 32 therefore b=4 and a=3.

Answered by Liam R. Maths tutor
3766 Views

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