Is the function f(x) = 5 + 3x a one-to-one function?
2007-04-10 15:45:57 · 5 answers · asked by TICKLES 1 in Science & Mathematics ➔ Mathematics
yes it is. the way you can tell is if you switch the x and the f(x) and then solve for x again.
x = 5 + 3*f(x)
x - 5 = 3*f(x)
(x - 5)/3 = f(x).
if a function's inverse is also a function, then it's one-to-one. in other words, if you can switch the variables around and still get f(x) on one side of the equation and everything else on the other side, then it's a one-to-one function.
2007-04-10 15:50:12 · answer #1 · answered by Anonymous · 0⤊ 1⤋
yes. f(x) will always have one and only one result for any value of x.
Pardon the delirium's explanation has a flaw. Try that with fx)=x^2 and under his explanation the answer would be yes, but this function is not a 1 to 1 function.
2007-04-10 23:02:51 · answer #2 · answered by felasbigdaddy 2 · 0⤊ 0⤋
Yes bacause that is a case of a linear function. Any linear equation is a function and a function has a one-to-one correspondence.
2007-04-10 22:53:46 · answer #3 · answered by Ernan D 1 · 1⤊ 0⤋
Yes. Suppose f(a) = f(b).
Then 5 + 3a = 5 + 3b
3a = 3b
a = b.
That means f is 1-1.
2007-04-10 22:51:35 · answer #4 · answered by steiner1745 7 · 0⤊ 0⤋
yes. Each point in x maps to only one point in f(x).
This is a linear function.
if x = 1, f(x) = 8, and for any x value there is only one f(x) corresponding value.
2007-04-10 22:51:42 · answer #5 · answered by looikk 4 · 1⤊ 0⤋