let function f:R to R be defined by f(x)=2x+sinx for real x. then f is
a) one to one and onto
b) one to one but not onto
c)onto but not onr to one
d) neither of the common tangent to the curves
I think this may be a bit backwards...? Doesn't "onto" mean "every y-value is 'covered'"...? Doesn't "one-to-one" mean "every y-value corresponds to only one x-value"...?
The conclusion remains the same, however.
Note to original poster: To show, using pre-calculus techniques, that no y-value is covered twice, you might be expected to try to find x-values having the same y-value, and then show that this is impossible. You might be expected to start with the slope formula, noting that the slope between these two (non-existant) points must be zero. Then:
. . . . .
Multiply through by the denominator to get:
. . . . .
. . . . .
. . . . .
. . . . .
But is this value possible?