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If you are given the function f(x) = 10-3x and g(x) = (x-3)/2 , find the value of the composite function gf(4) ?

The composite function can be thought of as if the function f(x) is the variable for the function g(x) instead of x. So first you find the value of the function f(4),f(4) = 10 - (3x4) = 10 - 12 = -2Now that ...
HL
Answered by Hajerah L. • Maths tutor
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How many (1/6)'s are there in 4 & 1/2?

The first step is to work out how many (1/6) there are in one whole. 6 x (1/6) = 1. 2)The next step uses partitioning. Split the 4 & (1/2) into a separate (4) and then (1/2) 3) Work out how many (1/6)'s ...
RM
Answered by Rimah M. • Maths tutor
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How do you differentiate y=ln(x)

I would use the fact that ln is the inverse function of the exponential function e^x to re-write the equation as x=e^y. This can be directly seen by just putting e^y=e^(lnx). Since the definition of a ln(a)=...
MG
Answered by Milo G. • Maths tutor
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Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2

First, use the identity cos(2x)=(cos(x))^2-(sin(x))^2 along with the identity (sin(x))^2+(cos(x))^2=1 to obtain the integral of 1/2*(1-cos(2x)) as it is not possible to integrate (sin(x))^2 straight off with...
TL
Answered by Thomas L. • Maths tutor
5558 Views

Solve the simultaneous equations..... 3x - y + 3 = 11 & 2x^2 + y^2 + 3 = 102 where X and Y are both positive integers.

Here we have two equations with two unknowns, the method we use to solve this is substitution. First, find one of the unknowns in terms of the other by rearranging the first equation to arrive at y = 3x - 8,...
RW
Answered by Reuben W. • Maths tutor
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