Let A = R – {3} and B = R – {1}. Consider the function f : A B defined by . Show that f is one-one and onto and hence find f - 1.
Find the point on the curve y = x3 – 11x + 5 at which the equation of tangent is y = x – 11.
The equation of the given curve is y = x3 - 11 x + 5.
The equation of the tangent to the given curve is given as y = x - 11 ( Which is of the form y = m x + c ).
Slope of the tangent = 1
Now, the slope of the tangent to the given curve at the point ( x, y ) is
given by,
Then, we have:
3 x2 - 11 = 1
When x = 2, y = ( 2 )3 - 11 ( 2 ) + 5
= 8 - 22 + 5
= - 9.
When x = - 2, y = ( - 2 )3 - 11 ( - 2 ) + 5
= - 8 + 22 + 5
= 19.
Hence, the required points are ( 2, - 9 ) and ( - 2, 19 ).
Using matrices solve the following system of linear equations:
x - y + 2 z = 7
3 x + 4 y - 5 z = - 5
2 x - y + 3 z = 12