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find the inverse function of the following: f(x) = 3x-5

in an inverse function, simply put the x and y are inversed: meaning x becomes y, and y becomes x f(x): y=3x-5 f-1(x): x=3y-5 <=> x+5=3y <=> (x+5)/3 = y <=> (1/3)x + (5/3) = y answer
OT
Answered by Olivia T. • Maths tutor
5411 Views

How do you integrate x* (exp(x))??

The easiest method to use in this incidence is integratation by parts. So let u=x and dv/dx=exp(x). Therefore du/dx=1 and v=exp(x). Then we use the formula where integral(u du/dx)=u v-integral(v*du/dx). So i...
HJ
Answered by Harmony J. • Maths tutor
11997 Views

Differentiate y=x^3*(x^2+1)

As this is a product of two functions it is necessary to use the product rule for differentiation. Therefore one of the functions must labeled v and the other u. i.e. u=x^3 and v=(x^2+1). It is then necessar...
BJ
Answered by Bevan J. • Maths tutor
4101 Views

A right-angled triangle has an angle of 30 degrees and its hypotenuse has a length of 9cm. Find the length of either of the triangle's other two sides.

Please note that this solution is easier to explain with 2 diagrams The side opposite of the 30 degree angle: If we have the hypotenuse and require the length of the opposite side then we would use sin ( Soh...
CB
Answered by Ciaran B. • Maths tutor
5369 Views

Given y = ln((2x+3)/(7x^3 +1)). Find dy/dx

y = ln(2x+3 / 7x^3 +1) d/dx(2x+3 / 7x^3 + 1) by quotient rule which is(v.du/dx - u.dv/dx) / v^2 where u=2x+3 and v=7x^3 +1 gives (-27x^3 -63x^2 +2) / (7x^3 +1)^2 so d/dx(ln(2x+3 / 7x^3 +1) = ( (-27x^3 -63x^2...
SB
Answered by Samuel B. • Maths tutor
4256 Views