Question

If f(x)=(x+5)/(3x-4) and t=(5+4x)/(3x-1) then f(t)= a) 1 b) x c) 2 d) 0​

Answer 1

Answer:

x  , which is option (b)

Step-by-step explanation:

given, f(x) = $\frac{(x+5)}{(3x-4)}$

also, t = $\frac{(5+4x)}{(3x-1)}$

so, f(t) = $\frac{( \frac{5+4x}{3x-1} )+5}{(3(\frac{5+4x}{3x-1}) -4)}$

          = $\frac { \frac{(5(3x-1)+(5+4x)}{3x-1} } {\frac{3(5+4x)-4(3x-1)}{3x-1} }$

          =  $\frac{(5(3x-1)+(5+4x)}{3x-1}$* $\frac{3x-1} {3(5+4x)-4(3x-1)}$

          = $\frac{15x-5+5+4x}{1}$ * $\frac{1} {15+12x-12x+4}$

          = $\frac{19x}{1}$ * $\frac{1} {19}$

          = x  , which is option (b)