Question

If f(x) = 2x – 5, then what is the value of f (2) + f (5)?
A) 1
B) 2
C) 3
D) 4

Answer 1

Hint:
Here we need to find the value of the given function at points $x=2$ and $x-5$. So, we’ll put x = 2 in f(x) to find f (2) and x = 5 in the f(x) to find f (5), then their addition will give us the answer.

Complete step by step solution:
f(x) = 2x – 5
Now, if we put x = 2
Then, this equation becomes
${\rm{f}}\left( 2 \right) = 2\left( 2 \right) - 5$ (i)
$ \Rightarrow {\rm{f}}\left( 2 \right) = 4 - 5 = - 1$

Again, When x = 5
$\therefore {\rm{f}}\left( {\rm{x}} \right) = 2{\rm{x}} - 5$
$ \Rightarrow {\rm{f}}\left( 5 \right) = 2 \times 5 - 5 = 10 - 5 = 5$ (ii)

Now, adding equation 1 and 2, we get
 ${\rm{f}}\left( 2 \right) + {\rm{f}}\left( 5 \right) = - 1 + 5$
 ${\rm{f}}\left( 2 \right) + {\rm{f}}\left( 5 \right) = 4$

∴ Answer is D i.e. 4.

Note:
In such questions sometimes, we have to find f (y), y $ \in $ R then just by putting some random values of x, we can find f(x) for different values of x and then you can solve according to the question.