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Water Cycle

Find g of and...

Question

Find gof and fog, if

(i)

(ii)

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Solution

(i)

(ii)

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g o f

f o g

f (x) = | x |

g (x) = | 5 x - 2 |

f (x) = 8 x^{3}

g (x) = x^{\frac{1}{3}}

Q. Find gof and fog when f : R → R and g : R → R are defined by
(i) f(x) = 2x + 3 and g(x) = x² + 5
(ii) f(x) = 2x + x² and g(x) = x³
(iii) f(x) = x² + 8 and g(x) = 3x³ + 1
(iv) f(x) = x and g(x) = |x|
(v) f(x) = x² + 2x − 3 and g(x) = 3x − 4
(vi) f(x) = 8x³ and g(x) = x¹^/3

g o f (x)

f (x) = 8 x^{3}

g (x) = x^{1 / 3}

Find gof and fog, if
$(i) f (x) = 8 x^{3}$ and $g (x) = x^{\frac{1}{3}}$ .

Q. Find fog and gof if
(i)

f (x) = e^{x}, g (x) = \log_{e} x

f (x) = x^{2}, g (x) = \cos x

f (x) = | x |, g (x) = \sin x

f (x) = x + 1, g (x) = e^{x}

f (x) = \sin^{- 1} x, g (x) = x^{2}

f (x) = x + 1, g (x) = \sin x

f (x) = x + 1, g (x) = 2 x + 3

f (x) = c, c \in R, g (x) = \sin x^{2}

f (x) = x^{2} + 2, g (x) = 1 - \frac{1}{1 - x}

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