Find the inverse of g(x)=5x-8

Would it be h(x)=x+8/5

looks good

But when I checked online it said g^-1(x)=x+8/5

g^-1 is notation for "inverse of g" ... is the name important?

so it's fine if i put h(x)

dunno - as scott asked: is the name important?

Unless you explain what h(x) is, it bears no relevance to the question.
If you say that h(x) = g^-1(x) then it should be fine.
But, that's even more work than just saying that g^-1(x) = x+8/5.

In fact, I'd just put x+8/5 since it is clear what they are asking for, not its name.

To find the inverse of a function, you need to switch the roles of x and y and solve for y.

Let's start with the function g(x) = 5x - 8.

1. Replace g(x) with y: y = 5x - 8.

2. Swap x and y: x = 5y - 8.

3. Solve for y: Add 8 to both sides of the equation: x + 8 = 5y.

4. Divide both sides by 5 to isolate y: (x + 8)/5 = y.

So, the inverse function of g(x) = 5x - 8 is h(x) = (x + 8)/5.

Therefore, your answer is correct. The inverse function is h(x) = (x + 8)/5.