Question

. If f(x) = 3x - 4 and g(x) = x + 4/ 3 then find fog and gof​

Answer 1

Answer:

fog=gof=x

Step-by-step explanation:

$fog = f(g(x)) = 3( \frac{x + 4}{3} ) - 4 \\ = x + 4 - 4 = x \\ gof = g(f(x)) = \frac{3x - 4 + 4}{3} \\ = \frac{3x}{3} =x \\ fog = gof = x$

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Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{f(x) = 3x - 4 \: \: \: and \: \: \: g(x) = \frac{x + 4}{3} }$

TO DETERMINE

$\displaystyle \sf{ f \circ g \: \: \: and \: \:g \circ f }$

EVALUATION

Here it is given that

$\displaystyle \sf{f(x) = 3x - 4 \: }$

$\displaystyle \sf{g(x) = \frac{x + 4}{3} }$

Now

$\displaystyle \sf{ (f \circ g )(x) }$

$\displaystyle \sf{ = f ( g (x) )}$

$\displaystyle \sf{ = f \bigg( \frac{x + 4}{3} \bigg)}$

$\displaystyle \sf{ = 3 \bigg( \frac{x + 4}{3} \bigg) - 4}$

$\displaystyle \sf{ = x + 4 - 4}$

$\displaystyle \sf{ =x}$

Again

$\displaystyle \sf{ (g \circ f )(x)}$

$\displaystyle \sf{ = g ( f (x))}$

$\displaystyle \sf{ = g \bigg( 3x - 4 \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{3x - 4+ 4}{3} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{3x }{3} \bigg)}$

$\displaystyle \sf{ = x}$

Thus we get

$\displaystyle \sf{ f \circ g (x) = g \circ f (x) = x}$

Additional Information :

In that case we say that f is inverse of g and g is inverse of f

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