Answer: Hello there!
A function only can have an inverse if the function is injective and surjective (and continuous):
Then we need to see; if f(x1) = f(x2) = y, and x1 is different from x2, then f(x) has not an inverse:
a) f(x) = Ix - 4I + 1
for example, f(0) = I-4I + 1 = 5
and f(8) = I8 -4I + 1 = 4 + 1 = 5
then f(x) does not have an inverse
b) f(x) = 25x^2 + 70x + 49
This is a cuadratic function, wich is graphed as a arc going up or down, wich means that there are two values of x that give the same value for f(x), then this function has not inverse. (this will be the case for all even powers)
c) f(x) = x^4
Again, an even power. But let's probe it:
f(1) = 1^4 = 1
f(-1) = (-1)^4 = 1
f(x) does not have an inverse:
d) f(x) = x + 3/7
Ok, here we have a linear equation, wich means that is injective and surjective.
The inverse of this function can be g(x) = x - 3/7
proof:
f(g(x)) = f( x - 3/7) = (x - 3/7) + 3/7 = x
then f and g are inverses of each other.
(if in this case f(x) = (x + 3)/7 = x/7 + 3/7 is also a linear equation, so it is injective and surjective (and continuous), wich implies that has an inverse)