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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 ).
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Answered by Alfie R. • Maths tutor
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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&qu...
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Answered by Tej T. • Maths tutor
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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 infini...
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Answered by Euan F. • Maths tutor
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f(x) = (sin(x))^3. What is f'(x)

Write sin 3 ( x ) as sin 2 x *sin x and differentiate using product rule, u =sin 2 x , v =sin x , d u /d x =2sinxcosx, d v /d x =cos x where the product rule is u (d v /d x ) + v (d u /d x ). This gets 2sin ...
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Answered by Liam R. • Maths tutor
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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.
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Answered by Liam R. • Maths tutor
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