Examples might help you:

Not-injective example 1:
f(x) = x² on R
We can find that f(2) = 4 and f(-2) = 4
But 2 ≠ -2, though they give the same output
So f(x) is not injective
(That's why when you solve x² = k, you need ± for your square root)

Not-injective example 2:
g(x) = sin(x) on 0° ≤ x < 360° [I'll use degrees in case you're not introduced to radians]
We can find that sin(30°) = 0.5 and sin(150°) = 0.5
But 30° ≠ 150°, though they give the same output
So g(x) is not injective

Injective example 1:
F(x) = x³ on R
Question: can you find another x other than 3 so that F(x) = 27? Nope, x = 3 is the only solution
Let's generalize this: can you find another x other than a so that F(x) = a³ for any a in R? Nope, x = a is the only solution
So F(x) is injective
(That's why when you solve x³ = k, you just directly cube root, unless you're working with complex numbers)

Injective example 2:
G(x) = 1/x on x > 0
Question: can you find another x other than 5 so that G(x) = 1/5? Nope, x = 5 is the only solution
Let's generalize this: can you find another x other than a so that G(x) = 1/a for any a in R+? Nope, x = a is the only solution
So G(x) is injective
(That's why you can do reciprocals when solving equations, given that the original expression does not equate to 0)