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If the functions f and g are defined: f: x--> x/5 + 4 g : x--> 30x + 10. what is x, if fg(x) = x. ?? What would fgf(x) = x^2 be??

You should insert function g into function f. (30x + 10) / 5 + 4 = 0 6x + 2 + 4 = 0 6x + 6 = 0 x = -1 This is a more complex problem:You need to do a similar task but you should do it in steps.gf(x) = 30 (x/...
LM
Answered by Lottie M. • Maths tutor
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Differentiate y = ln (3x + 2)

The equation for the derivative of the natural log is dy/dx = f'(x)/f(x) where f(x) = the contents of the natural log, in this case 3x+2. So, to get dy/dx we first need f'(x), the derivative of f(x). This is...
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Answered by Will S. • Maths tutor
22551 Views

Solve the simultaneous equations: y+4x+1=0 and y^2+5x^2+2x=0

y= -4x-1y 2 = (-4x-1) 2 = 16x 2 +8x +1y 2 +5x 2 +2x = 0lets substitute what we found y 2 equal to earlier, which gives us(16x 2 +8x +1) + 5x 2 +2x = 021x 2 + 10x +1 = 0after factorising this we get(7x+1)(3x+...
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Answered by Oleksandr U. • Maths tutor
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Solve int(ln(x)dx)

To solve this we must use integration by parts: int(udv) = uv - int(vdu) (1) Hence let u = ln(x), dv = dx => du=(1/x)dx, v=x, and now using (1) and substituting values we obtain int(ln(x)dx) = ln(x)x - in...
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Answered by George B. • Maths tutor
4002 Views

What is integration?

Integration can be viewed in many ways. The most common way to interpret an integral is to take the area under the curve you would like to integrate. For example Draw y=x, limit between 0 and 1, shade in the...
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Answered by Mikhail S. • Maths tutor
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