Find fog 2 and gof 1 when - f- R - R - fx-x2-8 and g- R - R - gx-3 x3-1-

Fog #160;2=f #160;g #160;2=f3 #215;23+1=f25=252+8=633gof #160;1=g #160;f #160;1=g #160;12+8=g #160;9=3 #215;93+1=2188 ...

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Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

Find fog 2 an...

Question

Find fog (2) and gof (1) when : f : R → R ; f(x) = x² + 8 and g : R → R; g(x) = 3x³ + 1.

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Solution

$(f o g) (2) = f (g (2)) = f (3 \times 2^{3} + 1) = f (25) = 25^{2} + 8 = 633 (g o f) (1) = g (f (1)) = g (1^{2} + 8) = g (9) = 3 \times 9^{3} + 1 = 2188$

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Similar questions

Q. Let f : R → R and g : R → R be defined by f(x) = x² and g(x) = x + 1. Show that fog ≠ gof.

Q. If the function

f : R \to R

be given by

f (x) = x^{2} + 2

and

g : R \to R

be given by

g (x) = \frac{x}{x - 1}, x \neq 1

, find fog and gof and hence find

f o g (2)

and

g o f (- 3)

If the function $f : R \to R$ be given by $f (x) = x^{2} + 2$ and $g : R \to R$ be given by $g (x) = \frac{x}{x - 1}, x \neq 1$ ,
find fog and gof and hence fing fog(2) and gof(-3).

Q. Let f : R → R and g : R → R be defined by f(x) = x + 1 and g(x) = x − 1. Show that fog = gof = I_R.

Q. Let f : R → R, g : R → R be two functions defined by f(x) = x² + x + 1 and g(x) = 1 − x². Write fog (−2).

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Find fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → R; g(x) = 3x3 + 1.

fog 2=f g 2=f3×23+1=f25=252+8=633gof 1=g f 1=g 12+8=g 9=3×93+1=2188

Find fog (2) and gof (1) when : f : R → R ; f(x) = x² + 8 and g : R → R; g(x) = 3x³ + 1.

$(f o g) (2) = f (g (2)) = f (3 \times 2^{3} + 1) = f (25) = 25^{2} + 8 = 633 (g o f) (1) = g (f (1)) = g (1^{2} + 8) = g (9) = 3 \times 9^{3} + 1 = 2188$