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

Integrating is essentially the opposite of differentiating.x n --> x n+1 We add 1 to the power and re-introduce variables where they have been eliminated potentially k --> kxWe must also take into acco...
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Answered by Joshua S. • Maths tutor
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