Question

1. If f(x)= x2 and g(x)= x - 7. Find:
(a) gof (b) fog (c) gog (d) fof​

Answer 1

Given :-

• f(x) = $\sf{\ x^{2}}$

• g(x) = x-7

Answer :-

• For finding these four value as will put the value of one into another to get the value of it .

• All four values will be different from each other

a) gof

We have to find g[f(x)]

$\implies$$\sf\ x^{2} -7$

b) fog

We have to find f[g(x)]

$\sf{\ (x-7)^{2}}$

$\implies$$\sf{\ x^{2}+49-14x}$

c) gog

We have to find g[g(x)]

$\sf{(x-7)-7}$

$\sf{x-7-7}$

$\implies$$\sf{x-14}$

d)

We have to Find f[f(x)]

$\sf{\ (\ x^{2})^{2}}$

$\implies$$\sf{\ x^{4}}$

Answer 2

Answer:

Given :-

$f(x) = \sf{\ x^{2}} x 2</p><p> g(x) = x-7</p><p>Answer :-</p><p>For finding these four value as will put the value of one into another to get the value of it .</p><p>All four values will be different from each other</p><p>a) gof</p><p>We have to find g[f(x)]</p><p>\implies⟹ \sf\ x^{2} -7 x 2 −7</p><p></p><p>b) fog</p><p>We have to find f[g(x)]</p><p>\sf{\ (x-7)^{2}} (x−7) 2</p><p> </p><p>\implies⟹ \sf{\ x^{2}+49-14x} x 2+49−14x</p><p></p><p>c) gog</p><p>We have to find g[g(x)]</p><p>\sf{(x-7)-7}(x−7)−7</p><p></p><p>\sf{x-7-7}x−7−7</p><p></p><p>\implies⟹ \sf{x-14}x−14</p><p></p><p>d)</p><p>We have to Find f[f(x)]</p><p>\sf{\ (\ x^{2})^{2}} ( x 2 ) 2\implies⟹ \sf{\ x^{4}} x 4$