XAT Functions, Graphs and Statistics questions

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

f is a function for which f(1)= 1 and f(x) = 2x + f(x - 1) for each natural number x$$\geq$$2. Find f(31)

Find the equation of the graph shown below. 

If $$f(x^2 - 1) = x^4 - 7x^2 + k_1$$ and $$f(x^3 - 2) = x^6 - 9x^3 +k_2$$ then the value of $$(k_2 - k_1)$$ is

For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:

The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is

The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?

The domain of the function $$f(x) =log_{7}({ log_{3}(log_{5}(20x-x^{2}-91 )))}$$ is:

Determine the value(s) of “a” for which the point $$(a, a^{2})$$ lies inside the triangle formed by the lines: 2x+ 3y= 1, x+ 2y=3 and 5x-6y= 1

The operation (x) is defined by
(i) (1) = 2
(ii)(x  + y) = (x).(y)

for all positive integers x and y.
If $$\sum_{x=1}^n(x)$$ = 1022 then n =

The y - ordinates of $$A_8$$ is

The number of point(s) satisfying the above mentioned characteristics and not in the first quadrant is/are