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How would you solve 4x > 7 - 10x ?

When solving an inequality, you want to get all of the x terms on one side, just like when you're solving an equation. Therefore, adding 10x to each side would give us:4x (+10x) > 7 - 10x (+10x) which ...

Answered by Sarah G. • Maths tutor

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Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0

2^2x - 6(2^x) + 5 = 0let y = 2^xy² - 6y + 5 = 0(y-5)(y-1) = 0 y=5, y=12^x= 5, therefore, x = log₂5 = 2.32 (3 s.f.)2^x = 1, therefo...

Answered by Jess O. • Maths tutor

4652 Views

Find the gradient of the function f(x,y)=x^3 + y^3 -3xy at the point (2,1), given that f(2,1) = 6.

Firstly, establish that the correct method to do this is via differentiation: specifically implicit differentiation. To find the gradient, we need to find dy/dx. The differential with res...

Answered by Daniel D. • Maths tutor

5763 Views

If f(x) = sin(2x)/(x^2) find f'(x)

As f(x) is in the form of u(x)/v(x) we can apply the rule that f'(x) = (u'(x)*v(x) - v'(x)*u(x))/(v(x)²), pulled from the C3 formula booklet.
If u(x) = sin(2x) then u'(x) = 2cos(2x).
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Answered by Leo R. • Maths tutor

3658 Views

The function f (x) is defined by f (x) = (1-x)/(1+x), x not equal to -1. Show that f(f (x)) = x. Hence write down f ^-1 (x).

f(f (x) )= f( (1-x)/(1+x) ) = (1-(1-x)/(1+x))/(1+(1-x)/(1+x))where you replace x by (1-x)/(1+x). Multiply the top and bottom of the fraction by (1+x) to get ((1+x)-(1-x))/((1+x)+(1-x)) which simplifies t...

Answered by Sarah P. • Maths tutor

11645 Views