Given `g(x)=(x+2)/(x-1)` and the line `3x+y-10=0.` Then the line is tangent to `g(x)` (b) normal to `g(x)` chord of `g(x)` (d) none of these

If f (x)=((x-1) (x-2))/((x-3)(x-4)), then number of local extremas for g (x) , where g (x) =f (|x|): (a) 3 (b) 4 (c) 5 (d) none of these

If g(x)=(2x+3)^(2) , then g((x)/(3)-1)=

Let f(x)=x^(3)+x+1 and let g(x) be its inverse function then equation of the tangent to y=g(x) at x = 3 is

f(x) ,g(x) and h(x) are all continuous and differentiable functions in [a,b] . Also altcltb and f(a)= g(a)=h(a ). Point of intersection of the tangent at x=c with chord joining x=a and x=b is on the left of c in y= f(x) and on the right in y=h(x) . And tangent at x=c is parallel to the chord in case of y=g(x) . Now answer the following questions. If c=(a+b)/(2) for each b , then:

Given that f(x) > g(x) for all real x, and f(0)=g(0) . Then f(x) < g(x) for all x belong to (a) (0,oo) (b) (-oo,0) (c) (-oo,oo) (d) none of these

If f(x)=x+tanx and g(x) is the inverse of f(x) , then differentiation of g(x) is (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)+x]^2) (c)1/(2+[g(x)-x]^2) (d) none of these

If g(x)=max(y^(2)-xy)(0le yle1) , then the minimum value of g(x) (for real x) is

If g(x)=int_0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where n in N , (a) g(x)+g(pi) (b) g(x)+g((npi)/(2)) (c) g(x)+g(pi/2) (d) none of these

Let f(x)=(sinx)/x and g(x)=|x.f(x)|+||x-2|-1|. Then, in the interval (0,3pi) g(x) is :