## anonymous one year ago Let h(x) = |kx+5|, domain of f(x) is [-5,7] , domain of f(h(x)) is [-6,1] and range of h(x) is the same as the domain f(x), then the value of k is

1. anonymous

@ganeshie8

2. ganeshie8

is the answer $$k\in [-\frac{1}{3},~~2]$$ ?

3. anonymous

its an mcq and options are 1/3 4/5 1 none

4. anonymous

and its a single correct

5. ganeshie8

domain of f(h(x)) is [-6,1]  |dw:1440520009960:dw|

6. ganeshie8

domain of f(x) is [-5,7] therefore we must have : -5 < h(x) < 7 does that look fine so far ?

7. anonymous

yep

8. ganeshie8

h(x) is absolute value function, so we don't need to wry about the lower bound -5

9. anonymous

thus 0

10. ganeshie8

we just need to make sure that h(x) is not greater than 7 in the interval [-6, 1]

11. ganeshie8

because f(x) becomes undefined for values greater than 7 |dw:1440520422396:dw|

12. anonymous

what if we try to draw the graph of h(x) with the vertex -5/k and y intercept (0,5) and draw two legs of the mod function and try to forcefully get the coordinates (1,7) from one part and from other ( -6,7) and take their intersection?

13. anonymous

I am still getting a range.. wbu?

14. ganeshie8