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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(7²+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(x²+ 1)" and "v = x² + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see &quo...

Answered by William P. • Maths tutor

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Translate the following text into German

I come from Leipzig, a city in the east of Germany. Before I was born, Germany was divided - the Federal Republic of Germany and the German Democratic Republic. There were two different political systems ...

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Predict the number of peaks in a carbon-13 NMR spectrum of the following carbonyl isomers of C5H8O. (i) CH3CH2CH2CH2CHO (ii) (CH3)3CCHO (iii) CH3COCH(CH3)2

(i) 5 peaks (ii) 3 peaks(iii) 4 peaks

Answered by Elizabeth D. • Chemistry 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^-1dy = xcos(x) dx∫y^-1dy = ∫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...

Answered by Abhiparth S. • Maths tutor

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