Question

Solve equation gf(x) = 1, when f(x)=4-3x and g(x)=
${3}^{ - x}$
​

Answer 1

Step-by-step explanation:

$f(x)=4-3x , g(x) = {3}^{ - x}$

$gf(x) = {3}^{ - (4 - 3x)}$

$1 = {3}^{ - 4 + 3x}$

$1 = {3}^{ - 4} \times {3}^{3x}$

$\frac{1}{ {3}^{ - 4} } = {3}^{3x}$

${3}^{4} = {3}^{3x}$

Comparing the index of both the terms

$4 = 3x$

$x = \frac{4}{3}$