Thank you so much for the explanation but honestly speaking , still I don't get it.
Please help me out.
Let's break this down into smaller pieces. I offered an approach that involved picking numbers. Ian offered an approach that involved algebra/number properties. Both are valid strategies when grappling with function questions.
First, let's make sure we understand the function.
When n is odd, f(n) = 3n - 9, and when n is even, f(n) = 2n - 7.
If you were picking numbers, you'd start with 5, as we're told the function is true for n > 4.
If n = 5, we're dealing with an odd, so f(n) = 3n - 9, or f(5) = 3*5 - 9 = 6.
So we know f(5) = 6.
If n = 6, we're dealing with an even, so f(n) = 2n - 7, or f(6) = 2*6 - 7 = 5.
So we know f(6) = 5.
If n = 7, we're back to odd, so f(7) = 3*7 - 9 = 12.
So we know f(7) = 12.
etc.
Put another way, we can understand functions in terms of inputs and outputs. If the input is 5, the output is 6. (When n = 5, f(5) = 6.)
Similarly, if the input is 6, the output is 5. (When n = 6, f(6) = 5.)
So I noted two things: first that when my input was ODD, my output was EVEN, and vice versa. And secondly, that when my inputs were smaller, they were close to the outputs.
Ian initially thought about the function in terms of number properties. If n = ODD, then f(n) = 3n - 9. Or f(ODD) = 3*ODD - 9.
3*ODD - 9 = ODD - ODD = EVEN
If n = EVEN, then f(n) = 2n - 7. or f(EVEN) = 2*EVEN - 7 = EVEN - ODD = ODD.
Again, we see that if the input is ODD, the output is EVEN and vice versa.
This is what we want to establish before evaluating the statements. Does that make sense so far? (If it does, I'll go ahead and evaluate the statements in a second post. If not, let's clarify any confusion first.)
