Question

F(ax+b) = cx+d
f(x)=?
​

Answer 1

To solve this problem, we need to substitute f(ax+b) into the expression for cxf(x):

cxf(x) = cxf(x)

Now, substitute ax+b for x in the right-hand side:

cxf(x) = cxf(ax+b)

We also know that f(ax+b) = cx+d, so we can substitute this expression for the right-hand side:

cxf(x) = c(f(ax+b)) + d

Now, substitute x back into the expression for f(ax+b):

cxf(x) = c(cx + d) + d

Simplifying this expression gives:

cxf(x) = ccx + cd + d

cx(f(x) - c) = cd + d

Finally, solve for f(x):

f(x) = c(x/f(x)) + d/f(x) + 1

Therefore, f(x) = (c/f(x))x + (d/f(x)) + 1.