Question

If f(x) = 1/1-x and g(x) = (x-1)/x, than fog(x) is​

Answer 1

Answer:

X

Step-by-step explanation:

fog(x)=fg(x)=f(x-1÷x)=f(1/1-x-1÷1/1-x)=x

Answer 2

GIVEN :

The functions f is defined by $f(x)=\frac{1}{1-x}$ and g is defined by $g(x)=\frac{x-1}{x}$

TO FIND :

The value of the composite function $(f\circ g)(x)$

SOLUTION :

The composite function of f and g is defined by $(f\circ g)(x)$

$(f\circ g)(x)=f(g(x))$

Since $g(x)=\frac{x-1}{x}$

$=f(\frac{x-1}{x})$

Since $f(x)=\frac{1}{1-x}$ put the value of x is $\frac{x-1}{x}$ in the function f(x)

$=\frac{1}{1-(\frac{x-1}{x})}$

$=\frac{1}{\frac{x-(x-1)}{x}}$

Using the distributive property :

a(x+y)=ax+ay

$=\frac{1}{\frac{x-1(x)-1(-1)}{x}}$

Adding the like terms

$=\frac{1}{\frac{x-x+1}{x}}$

$=\frac{1}{\frac{1}{x}}$

$=x$

∴ $(f\circ g)(x)=x$

Therefore the value of the composite function of f and g $(f\circ g)(x)$ is x

∴  $(f\circ g)(x)$ is x