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Let f (x) = 5x and g(x) = x2 + 1 , for x ∈  . (a) Find f-1(x) . (b) Find ( f ° g) (7) .

a,y=5xfinding the inverse: x=5y - dividing by 5 (1/5)x=y f -1 (x)=(1/5)x b,5x(7 2 +1)=250
Answered by • Maths tutor
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Differentiate f = ln(x^2 + 1) / (x ^ 2 + 1).

We'll apply the quotient rule using "u = ln(x 2 + 1)" and "v = x 2 + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see "v' = 2x". Now th...
WP
Answered by William P. • Maths tutor
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given that y = 1 when x = π, find y in terms of x for the differential equation, dy/dx = xycos(x)

y -1 dy = xcos(x) dx∫y -1 dy = ∫xcos(x) dx ln(y) = ∫xcos(x) dx [using integration by parts to integrate the right hand side] therefore, ln(y) = xsin(x) - ∫sin(x) dxln(y) = xsin(x) + cos(x) + cat y = 1, x = π...
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Answered by Abhiparth S. • Maths tutor
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Work out 2 3/4 x 1 1/2. Give your answer in terms of a mixed fraction in simplest form.

Step one: As the fractions are mixed fractions we need to convert them into top heavy fractions to multiply. 2 3/4 is equivalent to 11/4 ( as 2 3/4 = 4/4 + 4/4 + 3/4 = 11/4). 1 1/2 is equivalent to 3/2 (as 1...
MB
Answered by Megan B. • Maths tutor
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In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M= 300e^-0. 5t

The initial mass is found by putting t=0 into the given equation, so the initial mass is 300g. When the mass has decreased to half its value, M=150g. This gives us 150=300e^-0.05t, so e^-0.05t=1/2. Natural l...
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Answered by Theo T. • Maths tutor
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