Is this an Onto Function?
Let f : R → B is given by
f ( x ) = x 8 + 3 x 4 + 2 x 2 + 1 2 x 8 + 6 x 4 + 4 x 2 + 3
How many integral values does B includes for f ( x ) to be onto function?
Wanna try more problems on functions ?
The answer is 1.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Exactly. Also Range of f ( x ) is ( 2 , 3 ]
Log in to reply
sir how can we make graph of this function because graphical solutions are very attractive
Log in to reply
At x=0, the function will have maximum value i.e. 3 and As value of x will increase , the function will start decreasing and will tend to value of 2 at x tending to ∞ . You can y=2 line will be asymptote at the graph of f ( x ) . The graph will be symmetrical about y-axis, because of being e v e n function.
It is an even function And increasing the value of of x Decreases the function.
Exactly :)
exactly the same way :)
Yeah I think that was the only method to solve .....but who can tell there may be more..........😃
f ( x ) = x 8 + 3 x 4 + 2 x 2 + 1 2 ( x 8 + 3 x 4 + 2 x 2 + 1 ) + x 8 + 3 x 4 + 2 x 2 + 1 1
thus
f ( x ) = 2 + x 8 + 3 x 4 + 2 x 2 + 1 1
for f(x) to be integer x 8 + 3 x 4 + 2 x 2 + 1 1 should be an integer
solving it over reals we find the fraction becomes integer only for x = 0
therefore only one solution